In the given figure, WXYZ is a cyclic quadrilateral with WX parallel to YZ. If WXY = 50^\[\], find WOZ and YEZ where O is the center of the circle.

The angle $\angle WXY = 50^\circ$ is given. This angle is subtended by arc WY at point X on the circumference.
The angle $\angle WZY$ is also subtended by arc WY at point Z on the circumference.
Therefore, angles in the same segment are equal:

We are given that $WX \parallel YZ$.
Consider WZ as a transversal intersecting the